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Solve the quadratic equation $-x^2+7x-10=0$

Step-by-step Solution

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Final answer to the problem

$x=2,\:x=5$
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Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
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  • Find the derivative
  • Factor
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Can't find a method? Tell us so we can add it.
1

Factor the trinomial by $-1$ for an easier handling

$-\left(x^2-7x+10\right)=0$
2

Factor the trinomial $-\left(x^2-7x+10\right)$ finding two numbers that multiply to form $10$ and added form $-7$

$\begin{matrix}\left(-2\right)\left(-5\right)=10\\ \left(-2\right)+\left(-5\right)=-7\end{matrix}$
3

Thus

$-\left(x^2-7x+10\right)=0$
4

Factor the trinomial $\left(x^2-7x+10\right)$ finding two numbers that multiply to form $10$ and added form $-7$

$\begin{matrix}\left(-2\right)\left(-5\right)=10\\ \left(-2\right)+\left(-5\right)=-7\end{matrix}$
5

Thus

$-\left(x-2\right)\left(x-5\right)=0$
6

Multiply both sides of the equation by $-1$

$\left(x-2\right)\left(x-5\right)=0$
7

Break the equation in $2$ factors and set each equal to zero, to obtain

$x-2=0,\:x-5=0$
8

Solve the equation ($1$)

$x-2=0$
9

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-2$ from both sides of the equation

$x-2+2=0+2$
10

Canceling terms on both sides

$x=2$
11

Solve the equation ($2$)

$x-5=0$
12

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-5$ from both sides of the equation

$x-5+5=0+5$
13

Canceling terms on both sides

$x=5$
14

Combining all solutions, the $2$ solutions of the equation are

$x=2,\:x=5$

Final answer to the problem

$x=2,\:x=5$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $-x^2+7x-10$

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1
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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Quadratic Equations

The quadratic equations (or second degree equations) are those equations where the greatest exponent to which the unknown is raised is the exponent 2.

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